(b) [tex]\frac{25-2 u}{3}=2[/tex]
Answer (2)
Multiply both sides by 3: 25 − 2 u = 6 .
Subtract 25 from both sides: − 2 u = − 19 .
Divide both sides by -2: u = 2 19 .
The solution is 2 19 .
Explanation
Understanding the Problem We are given the equation 3 25 − 2 u = 2 Our goal is to solve for u .
Eliminating the Fraction First, we multiply both sides of the equation by 3 to eliminate the fraction: 3 × 3 25 − 2 u = 3 × 2 25 − 2 u = 6
Isolating the Term with u Next, we subtract 25 from both sides of the equation to isolate the term with u :
25 − 2 u − 25 = 6 − 25 − 2 u = − 19
Solving for u Now, we divide both sides by -2 to solve for u :
− 2 − 2 u = − 2 − 19 u = 2 19 We can also express this as a decimal: u = 9.5
Final Answer Therefore, the solution to the equation is u = 2 19 or u = 9.5 .
Examples
Imagine you're baking a cake and need to adjust a recipe. The recipe calls for a certain amount of flour, but you want to use a different sized pan. Solving equations like this helps you determine the exact amount of each ingredient needed to maintain the correct proportions and ensure your cake turns out perfectly. This type of problem is also useful in chemistry when you need to calculate the amount of reactants needed for a chemical reaction.
To solve the equation 3 25 − 2 u = 2 , we multiply both sides by 3, isolate the term with u , and divide to find u = 2 19 or u = 9.5 .
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